arXiv subjects

Tarik Dzanic

Publications and source records attributed to Tarik Dzanic.

24 records · Page 2Linked to original sources

arXiv2022

Positivity-Preserving Entropy-Based Adaptive Filtering for Discontinuous Spectral Element Methods

In this work, we present a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. By adapting the filter strength to enforce positivity and a local discrete minimum entropy principle, the resulting approach can robustly resolve strong discontinuities with sub-element resolution, does not require problem-dependent parameter tuning, and can be easily implemented on general unstructured meshes with relatively low computational cost. The efficacy of the approach is shown in numerical experiments on hyperbolic and mixed hyperbolic-parabolic conservation laws such as the Euler and Navier-Stokes equations for problems including extreme shocks, shock-vortex interactions, and complex compressible turbulent flows.

math.NA↗

arXiv2022

Utilizing Time-Reversibility for Shock Capturing in Nonlinear Hyperbolic Conservation Laws

In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time in the vicinity of shocks. The proposed approach does not require any additional governing equations or a priori knowledge of the hyperbolic system in question, is independent of the mesh and approximation order, and requires the use of only one tunable parameter. The primary novelty is that the resulting artificial viscosity is unique for each component of the conservation law which is advantageous for systems in which some components exhibit discontinuities while others do not. The efficacy of the method is shown in numerical experiments of multi-dimensional hyperbolic conservation laws such as nonlinear transport, Euler equations, and ideal magnetohydrodynamics using a high-order discontinuous spectral element method on unstructured grids.

math.NA↗

arXiv2021

Partially-Averaged Navier-Stokes Simulations of Turbulence Within a High-Order Flux Reconstruction Framework

High-order methods and hybrid turbulence models have independently shown promise as means of decreasing the computational cost of scale-resolving simulations. The objective of this work is to develop the combination of these methods and analyze the effects of high-order discretizations on hybrid turbulence models, particularly with respect the optimal model parameters and the relative accuracy benefits compared to approaches such as under-resolved direct numerical simulation (URDNS). We employ the Partially-Averaged Navier-Stokes (PANS) approach using the flux reconstruction scheme on the flow around a periodic hill and the wake flow of a circular cylinder at a Reynolds number of 3900, the latter of which we provide direct numerical simulation results and novel statistical analysis. By increasing the order of the discretization while fixing the total degrees of freedom, it was observed that larger improvements in the prediction of the statistics and flow physics were generally seen with PANS than URDNS. Furthermore, less sensitivity to the resolution-control parameter was observed with a high-order discretization, indicating that high-order discretizations may be an effective approach for increasing the accuracy and reliability of hybrid turbulence models for scale-resolving simulations without a significant increase in computational effort.

physics.flu-dyn↗

arXiv2020

A Riemann Difference Scheme for Shock Capturing in Discontinuous Finite Element Methods

We present a novel structure-preserving numerical scheme for discontinuous finite element approximations of nonlinear hyperbolic systems. The method can be understood as a generalization of the Lax-Friedrichs flux to a high-order staggered grid and does not depend on any tunable parameters. Under a presented set of conditions, we show that the method is conservative and invariant domain preserving. Numerical experiments on the Euler equations show the ability of the scheme to resolve discontinuities without introducing excessive spurious oscillations or dissipation.

math.NA↗

arXiv2020

Fourier Spectrum Discrepancies in Deep Network Generated Images

Advancements in deep generative models such as generative adversarial networks and variational autoencoders have resulted in the ability to generate realistic images that are visually indistinguishable from real images, which raises concerns about their potential malicious usage. In this paper, we present an analysis of the high-frequency Fourier modes of real and deep network generated images and show that deep network generated images share an observable, systematic shortcoming in replicating the attributes of these high-frequency modes. Using this, we propose a detection method based on the frequency spectrum of the images which is able to achieve an accuracy of up to 99.2% in classifying real and deep network generated images from various GAN and VAE architectures on a dataset of 5000 images with as few as 8 training examples. Furthermore, we show the impact of image transformations such as compression, cropping, and resolution reduction on the classification accuracy and suggest a method for modifying the high-frequency attributes of deep network generated images to mimic real images.

eess.IV↗

arXiv2020

Accuracy, Stability, and Performance Comparison between the Spectral Difference and Flux Reconstruction Schemes

We report the development of a discontinuous spectral element flow solver that includes the implementation of both spectral difference and flux reconstruction formulations. With this high order framework, we have constructed a foundation upon which to provide a fair and accurate assessment of these two schemes in terms of accuracy, stability, and performance with special attention to the true spectral difference scheme and the modified spectral difference scheme recovered via the flux reconstruction formulation. Building on previous analysis of the spectral difference and flux reconstruction schemes, we provide a novel nonlinear stability analysis of the spectral difference scheme. Through various numerical experiments, we demonstrate the additional stability afforded by the true, baseline spectral difference scheme without explicit filtering or de-aliasing due to its inherent feature of staggered flux points. This arrangement leads to favorable suppression of aliasing errors and improves stability needed for under-resolved simulations of turbulent flows.

physics.comp-ph↗